Suppose {X(t),t 0} is the standard Brownian process, its corresponding reflected Brownian process is defined by

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Suppose {X(t),t ≥ 0} is the standard Brownian process, its corresponding reflected Brownian process is defined by 

Y(t) = X(t), t 0.

Show that Y(t) is also Markovian and its mean and variance are, respectively, 

and E[Y]: var(Y) = Tale 2t  2 = (-) . 1 t.

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